If we are going to cherry-pick, we can begin by saying the OP Title is a meaningless statement.

"The perpetual *motion* of Evolution".

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Motion?

I believe a better statement would be; "the perpetual *function* of Evolution", And then I hope my posts are probative of those functions, not of motions, which clouds the underlying principle that evolution is a fundamental universal *function*.

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If we are going to cherry-pick, we can begin by saying the OP Title is a meaningless statement. Motion?

I believe a better statement would be; "the perpetual *function* of Evolution", And then I hope my posts are probative of those functions, not of motions, which clouds the underlying principle that evolution is a fundamental universal *function*.

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Nothing about "cherry-picking" here. You made a specific statement. I challenged it and asked you to justify it. And you can't. You were talking, not for the first time, out of your arse.

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One thing is abundantly clear, Evolution itself follows a probabilistic variable self-iterating fractal function. As the fractal function allows for expression in our reality the number of variables is unlimited, with the caveat ; subject to the probabilistic function of *natural selection*.

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Is this the statement you are referring to?

This proposition may be poorly constructed, but where does it fail in current scientific knowledge?

This proposition may be poorly constructed, but where does it fail in current scientific knowledge?

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Unless you can:

(a) state what "fractal function" you are referring to,
(b) explain what variables and constants in its algebra relate to elements of an evolutionary process, and
(c) provide evidence that this fractal function does actually model some aspect of the evolutionary process,

Unless you can:
(a) state what "fractal function" you are referring to,
(b) explain what variables and constants in its algebra relate to elements of an evolutionary process, and
(c) provide evidence that this fractal function does actually model some aspect of the evolutionary process,

There is some disagreement amongst authorities about how the concept of a fractal should be formally defined. Mandelbrot himself summarized it as "beautiful, damn hard, increasingly useful. That's fractals."

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The general consensus is that theoretical fractals are infinitely self-similar,

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iterated, and detailed mathematical constructs having fractal dimensions, of which many examples have been formulated and studied in great depth.

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The study of *fractal systems*

Fractals are not limited to geometric patterns, but can also describe processes in time.

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See Causal Dynamical Triangulation (CDT).

Fractal patterns with various degrees of self-similarity have been rendered or studied in images, structures and sounds and found in

While it is true that organisms do employ fractal geometry in their construction (the venerable fern leaf being a common example), I don't really see how it informs the topic of evolution itself, any more than pointing out that many organisms use sunlight and photosynthesis, or methanogenesis.

(c) provide evidence that this fractal function does actually model some aspect of the evolutionary process,

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See the illustrations.

Exchemist said,
This has nothing to do with what you were claiming about evolution, though!
This is about natural processes of growth.

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Two different things.[/QUOTE] Correct, growth is an important part of the evolutionary process, but it does not define fractality. See above.

b) explain what variables and constants in its algebra relate to elements of an evolutionary process.

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The variable aspect is introduced by Hazen, such as the wrong (but compatible) chemical being introduced into the replication, which alters its properties, and often degenerates the growth process, but occasionally enhances the growing structure. Evolution.

If you read back, I believe Hazen addressed such "variables" in his lecture, such as mutations which can be either detrimental or instrumental to the evolution of an organism.

While it is true that organisms do employ fractal geometry in their construction (the venerable fern leaf being a common example), I don't really see how it informs the topic of evolution itself, any more than pointing out that many organisms use sunlight and photosynthesis, or methanogenesis.

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These terms have been defined in many different ways and examples..

The problem most people struggle with is not HOW it works, but WHY it works that way.
There's the rub.

We know that Evolution is true from the studies of "how" evolution works, in order to arrive at the answer, "Why does it work at all?"

Max Tegmark explains *how* the universe functions mathematically. His conclusion is that a mathematical function is *why* the universe is able to function as it does.

Renate Loll (CDT) proposes that this mathematical function at every scale displays a fractal structure.

This means that it does not assume any pre-existing arena (dimensional space), but rather attempts to show how the spacetime fabric itself evolves.

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The Why.
I agree with the concept that the fractal function is the mathematical function which allows for evolution of the universe and everything in it and can be found in ALL forms of change or growth. The Fibonacci sequence is but one fractal form and can be observed throughout the universe and our world.

IOW, the universe functions mathematically in general, and fractal mathematics play a major role in the evolution of all things.

While you're at ridiculing Tegmark (Shapiro), you might also add this autobiography of Renate Loll, (CDT), another scientist who has a hypothesis, based on out of the box thinking. http://www.hef.ru.nl/~rloll/Web/title/title.html, another dreamer

Oh, the charlatans we can find lately.! Is there anyone left who can contribute something of value?

One thing I find encouraging, is that neither Tegmark's, nor Loll's hypotheses are in conflict with GR or QM, which, to my understanding is an important aspect of all theoretical science, especially in the area of cosmology and universal mathematical functions.

I find a certain comfort in that and to call their work nonsense isat the very least premature.

While it is true that organisms do employ fractal geometry in their construction (the venerable fern leaf being a common example), I don't really see how it informs the topic of evolution itself, any more than pointing out that many organisms use sunlight and photosynthesis, or methanogenesis.

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Thanks for the confirmation.
My thinking is based on the following.
If millions of years of natural selection seeking maximum benefits from photosynthesis eventually ends up with a fractal structure, I would call that proof of the efficiency of fractal functions. They exist in reality and are part of the evolutionary process.

I don't think that the constant elaboration of new species is all that mysterious. (What is a species? A 'natural kind'? Defining the word 'species' is still an outstanding problem in the philosophy of biology, the so-called 'species problem'.) If change is occurring for molecular biological reasons in the heritable molecular genetic material (the DNA code), then changes are going to accumulate over time into lineages, which will branch into sublineages, and on and on.

When we look at the phylogenetic 'tree of life', it appears to be a relentless expansion into an abstract possibility-space. Natural selection basically trims down that luxuriant tree, restricting it to viable forms and shaping it to the environment.

I don't think that it's in any way unreasonable to compare the tree of life to a fractal. Many people have made that association, it's nothing new. It does look the same on different scales. Anyone who has looked at the Mendlebrot set or Julia sets will recognize this -

And no, it needn't have anything to do with Mark Tegmark's mathematical metaphysics or with the totally irrelevant harping on the fact that Tegmark chose to use his mother's last name (maybe there was an unpleasant divorce, it's none of my business). I think that Write4U is correct about the tree of life's fractal geometry. Noting that certainly isn't an occasion for insults or put-downs. It's entirely relevant to this thread.